matita/matita/contribs/lambdadelta/basic_2A/reduction/cnr_crr.ma

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  14
  15 include "basic_2A/reduction/crr.ma".
  16 include "basic_2A/reduction/cnr.ma".
  17
  18 (* NORMAL TERMS FOR CONTEXT-SENSITIVE REDUCTION *****************************)
  19
  20 (* Advanced inversion lemmas on reducibility ********************************)
  21
  22 (* Note: this property is unusual *)
  23 lemma cnr_inv_crr: ∀G,L,T. ⦃G, L⦄ ⊢ ➡ 𝐑⦃T⦄ → ⦃G, L⦄ ⊢ ➡ 𝐍⦃T⦄ → ⊥.
  24 #G #L #T #H elim H -L -T
  25 [ #L #K #V #i #HLK #H
  26   elim (cnr_inv_delta … HLK H)
  27 | #L #V #T #_ #IHV #H
  28   elim (cnr_inv_appl … H) -H /2 width=1 by/
  29 | #L #V #T #_ #IHT #H
  30   elim (cnr_inv_appl … H) -H /2 width=1 by/
  31 | #I #L #V #T * #H1 #H2 destruct
  32   [ elim (cnr_inv_zeta … H2)
  33   | elim (cnr_inv_eps … H2)
  34   ]
  35 |5,6: #a * [ elim a ] #L #V #T * #H1 #_ #IH #H2 destruct
  36   [1,3: elim (cnr_inv_abbr … H2) -H2 /2 width=1 by/
  37   |*: elim (cnr_inv_abst … H2) -H2 /2 width=1 by/
  38   ]
  39 | #a #L #V #W #T #H
  40   elim (cnr_inv_appl … H) -H #_ #_ #H
  41   elim (simple_inv_bind … H)
  42 | #a #L #V #W #T #H
  43   elim (cnr_inv_appl … H) -H #_ #_ #H
  44   elim (simple_inv_bind … H)
  45 ]
  46 qed-.